A fuel break off element realized in the form of an even, thin plate having numerous curved, narrow slots on a fuel injector downstream from a dosing opening is already known from Unexamined German Patent Application No. 27 23 280. The geometric dimensions (i.e., radial width and curve length) of the curved slots, which are produced in the plate by etching, assure that a fuel veil is formed which breaks out in small droplets. The curved slots that are always arranged in groups break up the fuel according to their geometry which is produced horizontally. The individual slot groups must be produced very exactly in relation to one other so that the fuel is broken off in the desired manner. The curved slots each have a constant opening width over the entire axial extent of the break-off element. The inherent danger of this slot configuration is that "drops" will recombine to form larger drops.